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Towards a Theory of Dynamic Economic DevelopmentA Brief Overview of Cycle ModellingLike Marx, Keynes failed to formalise a complete theory of dynamic economic development or of its components, growth and business cycles. It is a testament to the magnitude of the problem that these two great economic and social thinkers were unable to formulate such a theory. The consequence has been numerous attempts by their disciples to complete their work.1 Keynesians have tended to seek separate theories of growth and the business cycle while Marxians have attempted to move beyond their initial preoccupation with crises towards an integrated theory of cycles and growth, but they have failed to agree on a common theory. Meanwhile the work of Schumpeter (1934, 1939), who came much closer to developing a complete theory of dynamic economic development, has largely been ignored in postwar business cycle literature. It has not, however, been ignored in the longcycle literature that proliferated since the early 1970s (see note 31). There is no space to review this literature here, but Schumpeter's contribution will be discussed in the next section and Shackle's related work will be discussed in section 4.4. Both of these great economists stressed the role of innovations in the generation of business cycles. Having seen early drafts of Keynes's General Theory, Harrod (1936) produced a Keynesian theory of the trade cycle in the same year as Keynes's book was published. His theory was based on multiplieraccelerator interaction. Harrod (1948) went on to concentrate on growth theory but his work on cycles was developed by Samuelson (1939), who demonstrated the various dynamic paths that could be derived from a linear deterministic multiplieraccelerator model. Earlier work by Frisch (1933) and Slutsky (1937) had shown the possibility of converting a series of random shocks, or impulses, into a cycle using a linear propagation model that displayed a damped monotonic or cyclical path in response to a single disturbance (see section 1.4). If linear stochastic models are to be employed, the basic choice is between FrischSlutsky models and explosive paths constrained by ceilings and floors, such as Hicks (1950), which also employed multiplieraccelerator interaction to give the essential dynamics. In the 1950s a number of nonlinear deterministic models were developed.3 Goodwin (1951), for example, employed a nonlinear accelerator to generate a limit cycle solution (see section 2.3 on limit cycles). The Hicks (1950) model can also be regarded as a nonlinear model which incorporates what Samuelson (1947) dubbed 'billiard table' nonlinearities and what we have called 'type I' nonlinearities.4 Other examples of such models are Smithies (1957) and Minsky (1959), which employ Duesenberrytype ratchet effects (Duesenberry 1949) on consumption expenditure within a basic multiplieraccelerator framework. Goodwin (1951), however, employed a nonlinear accelerator function, or 'type II' nonlinearity to generate cycles.5 These nonlinear models were capable of producing cycles that repeated themselves in the absence of shocks and consequently introduced the possibility of developing models in which the cycle was endogenously generated. They also allowed for the possibility of asymmetric expansionary and contractionary phases, which are not permitted in linear formulations (see section 1.3). Further, in the case of stable limit cycle solutions, shocks can be added to explain the observed irregularity in business cycles. Also in the 1950s, Goodwin (1955) and Kaldor (1954), among others, became concerned about the separation of cycle and growth theory. The Hicks (1950) assumption of a trend in autonomous investment seemed artificial. They felt that the role of innovation in stimulating growth, as stressed by Schumpeter (1934, 1935, 1939), had been overlooked and that undue stress had been placed on investment induced via the accelerator process. The Schumpeterian bunching of innovatory investment had been ignored. Goodwin and Kaldor expressed the view that a theory of dynamic economic development was required and that it was incorrect to decompose economic time series into a linear trend and cyclical fluctuations and to try to explain them separately, because they were part of the same process. The Keynesian structural econometric models built between the late 1950s and the early 1970s tended to display extreme monotonic, rather than cyclical, dampening. Adelman and Adelman (1959) found that autocorrelated, rather than random, shocks were required to generate realistic cycles.6 'Type I' and 'type II' nonlinearities were largely ignored in these models and by the end of the 1960s the very existence of business cycles was being questioned.7 Others, following Fisher (1925) (see section1.2) argued that it had never really existed because it represented the summation of random events with no propagation model transforming them into regular and repeated cycles. Interest in the business cycle was rekindled as a result of the response of OECD countries to the 1973 oil price shock and in the mid1970s two papers were published, Nordhaus (1975) and Lucas (1975),8 which stimulated renewed academic interest in the subject. Lucas's work seems to have had the more lasting impact and has led to numerous attempts to model the cycle as an equilibrium phenomenon (see section 2.2). Most of the work is in the FrischSlutsky tradition with a linear model propagating cycles in response to a series of random shocks. The cycle so formulated is, therefore, not endogenous and selfsustaining. This period also saw a resurgence of interest in long waves with speculation that the long postwar upswing had given way to the downswing of the long wave in the 1970s  see Mandel (1980) and Van Duijn (1983). The major debate in the 1980s was not over whether the FrischSlutsky modelling strategy was correct, but over the most important sources of shocks. Lucas (1975) had stressed the importance of monetary shocks but in the 1980s attention turned to real shocks as the major source of impulses. Lucas (1987) suggested a synthesis of the real and monetary equilibrium business cycle approaches which he feels should build on the Kydland and Prescott (1982) contribution (see section 2.2). The latter generates cycles using a stochastic derivative of the neoclassical growth model and as such marks a renewed attempt to integrate cycle and growth theory. A parallel development in the 1980s was the attempt by New Keynesians to derive microeconomic theories to explain wage stickiness and the various other planks on which Keynesian macroeconomic theory was built and, in so doing, to provide a rationalisation for disequilibrium theories of the cycle inspired by Keynes. Greenwald and Stiglitz (1987) assess the progress of the New Keynesian approach to business cycle modelling,9 which they note is in the FrischSlutsky tradition. External and internal shocks, in the form of shifts in Keynesian 'animal spirits' that arise from modelling under uncertainty rather than risk,10 drive the cycle, which is propagated by a Keynesian disequilibrium model with wage and price stickiness and information imperfections. No endogenous theory of the cycle has been developed and no theory of cyclical growth or dynamic economic development is presented in line with the theory towards which Keynes was groping. The stochastic linear multiplieraccelerator, the linear equilibrium business cycle and the emerging New Keynesian models are all, therefore, based on the FrischSlutsky approach and do not attempt to provide an endogenous theory of the cycle. They all utilise essentially linear propagation models to convert random or serially correlated shocks into cycles. Nonlinearities can, however, be used to generate endogenous cycles which can be regarded as the equilibrium motion of the economy. Recent demonstrations of this fact are due to Chiarella (1986) and Grandmont (1985), who uses nonlinearity to derive a truly equilibrium, in the sense that the cycle is the equilibrium motion and markets clear continuously, theory of the cycle (see section 2.3). Normally, however, the nonlinear models employ time trends to explain the movement of the point around which the limit cycle occurs. Even with nonlinear models, the full integration of cycles and growth remains a problem. In an attempt to achieve such an integration, numerous economists have extended the Goodwin (1967) predatorprey model (see section 2.3), which relied on trends in technical progress and the working population to generate growth. Some have, for example, tried to introduce endogenous technical progress. Goodwin stressed the need for a more disaggregated approach and in section 4.5 his recent work, published in Goodwin and Punzo (1987), will be discussed. In order to develop an integrated theory of cycles and growth it may be necessary to look to Schumpeter for inspiration, as Goodwin and Kaldor suggested in the 1950s and as longcycle theorists have done since the early 1970s. Shackle (1938) had already developed a theory which integrated Keynesian and Schumpeterian ideas with a Duesenberrytype 'ratchet effect' on consumption. Shackle's work on the cycle has been largely neglected. In order to rectify this, his work on the business cycle will be reviewed in section 4.4. First, however, Schumpeter's contribution to business cycle theory will be briefly discussed to provide a background for the discussion of Shackle's work and the subsequent contribution of Goodwin (section 4.5). 
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